Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for discrete density estimation tasks. However, large PCs are susceptible to overfitting, and only a few regularization strategies (e.g., dropout, weight-decay) have been explored. We propose HyperSPNs: a new paradigm of generating the mixture weights of large PCs using a small-scale neural network. Our framework can be viewed as a soft weight-sharing strategy, which combines the greater expressiveness of large models with the better generalization and memory-footprint properties of small models. We show the merits of our regularization strategy on two state-of-the-art PC families introduced in recent literature -- RAT-SPNs and EiNETs -- and demonstrate generalization improvements in both models on a suite of density estimation benchmarks in both discrete and continuous domains.

An outlier is an event or observation that is defined as an unusual activity, intrusion, or a suspicious data point that lies at an irregular distance from a population. The definition of an outlier event, however, is subjective and depends on the application and the domain (Energy, Health, Wireless Network, etc.). It is important to detect outlier events as carefully as possible to avoid infrastructure failures because anomalous events can cause minor to severe damage to infrastructure. For instance, an attack on a cyber-physical system such as a microgrid may initiate voltage or frequency instability, thereby damaging a smart inverter which involves very expensive repairing. Unusual activities in microgrids can be mechanical faults, behavior changes in the system, human or instrument errors or a malicious attack. Accordingly, and due to its variability, Outlier Detection (OD) is an ever-growing research field. In this chapter, we discuss the progress of OD methods using AI techniques. For that, the fundamental concepts of each OD model are introduced via multiple categories. Broad range of OD methods are categorized into six major categories: Statistical-based, Distance-based, Density-based, Clustering-based, Learning-based, and Ensemble methods. For every category, we discuss recent state-of-the-art approaches, their application areas, and performances. After that, a brief discussion regarding the advantages, disadvantages, and challenges of each technique is provided with recommendations on future research directions. This survey aims to guide the reader to better understand recent progress of OD methods for the assurance of AI.

Owing to the benefits for customers (lower prices), drivers (higher revenues), aggregation companies (higher revenues) and the environment (fewer vehicles), on-demand ride pooling (e.g., Uber pool, Grab Share) has become quite popular. The significant computational complexity of matching vehicles to combinations of requests has meant that traditional ride pooling approaches are myopic in that they do not consider the impact of current matches on future value for vehicles/drivers. Recently, Neural Approximate Dynamic Programming (NeurADP) has employed value decomposition with Approximate Dynamic Programming (ADP) to outperform leading approaches by considering the impact of an individual agent's (vehicle) chosen actions on the future value of that agent. However, in order to ensure scalability and facilitate city-scale ride pooling, NeurADP completely ignores the impact of other agents actions on individual agent/vehicle value. As demonstrated in our experimental results, ignoring the impact of other agents actions on individual value can have a significant impact on the overall performance when there is increased competition among vehicles for demand. Our key contribution is a novel mechanism based on computing conditional expectations through joint conditional probabilities for capturing dependencies on other agents actions without increasing the complexity of training or decision making. We show that our new approach, Conditional Expectation based Value Decomposition (CEVD) outperforms NeurADP by up to 9.76% in terms of overall requests served, which is a significant improvement on a city wide benchmark taxi dataset.

Google is paying tribute Tuesday to the computer scientist who created the mathematical framework "fuzzy logic." On this day in 1964, Zadeh submitted the paper "Fuzzy Sets," which laid out the concept of "fuzzy logic." The logo featured on Google.com "The theory he presented offered an alternative to the rigid'black and white' parameters of traditional logic and instead allowed for more ambiguous or'fuzzy' boundaries that more closely mimic the way humans see the world," reads a biography of Zadeh by Google. The theory has been used in various tech applications, including anti-skid algorithms for cars.

Power curves capture the relationship between wind speed and output power for a specific wind turbine. Accurate regression models of this function prove useful in monitoring, maintenance, design, and planning. In practice, however, the measurements do not always correspond to the ideal curve: power curtailments will appear as (additional) functional components. Such multivalued relationships cannot be modelled by conventional regression, and the associated data are usually removed during pre-processing. The current work suggests an alternative method to infer multivalued relationships in curtailed power data. Using a population-based approach, an overlapping mixture of probabilistic regression models is applied to signals recorded from turbines within an operational wind farm. The model is shown to provide an accurate representation of practical power data across the population.

We propose a new approach to explain Bayesian Networks. The approach revolves around a new definition of a probabilistic argument and the evidence it provides. We define a notion of independent arguments, and propose an algorithm to extract a list of relevant, independent arguments given a Bayesian Network, a target node and a set of observations. To demonstrate the relevance of the arguments, we show how we can use the extracted arguments to approximate message passing. Finally, we show a simple scheme to explain the arguments in natural language.

It is more flexible for decision makers to evaluate by interval-valued q-rung orthopair fuzzy set (IVq-ROFS),which offers fuzzy decision-making more applicational space. Meanwhile, Choquet integralses non-additive set function (fuzzy measure) to describe the interaction between attributes directly.In particular, there are a large number of practical issues that have relevance between attributes.Therefore,this paper proposes the correlation operator and group decision-making method based on the interval-valued q-rung orthopair fuzzy set Choquet integral.First,interval-valued q-rung orthopair fuzzy Choquet integral average operator (IVq-ROFCA) and interval-valued q-rung orthopair fuzzy Choquet integral geometric operator (IVq-ROFCG) are inves-tigated,and their basic properties are proved.Furthermore, several operators based on IVq-ROFCA and IVq-ROFCG are developed. Then, a group decision-making method based on IVq-ROFCA is developed,which can solve the decision making problems with interaction between attributes.Finally,through the implementation of the warning management system for hypertension,it is shown that the operator and group decision-making method proposed in this paper can handle complex decision-making cases in reality, and the decision result is consistent with the doctor's diagnosis result.Moreover,the comparison with the results of other operators shows that the proposed operators and group decision-making method are correct and effective,and the decision result will not be affected by the change of q value.

Changepoint analysis deals with unsupervised detection and/or estimation of time-points in time-series data, when the distribution generating the data changes. In this article, we consider \emph{offline} changepoint detection in the context of large scale textual data. We build a specialised temporal topic model with provisions for changepoints in the distribution of topic proportions. As full likelihood based inference in this model is computationally intractable, we develop a computationally tractable approximate inference procedure. More specifically, we use sample splitting to estimate topic polytopes first and then apply a likelihood ratio statistic together with a modified version of the wild binary segmentation algorithm of Fryzlewicz et al. (2014). Our methodology facilitates automated detection of structural changes in large corpora without the need of manual processing by domain experts. As changepoints under our model correspond to changes in topic structure, the estimated changepoints are often highly interpretable as marking the surge or decline in popularity of a fashionable topic. We apply our procedure on two large datasets: (i) a corpus of English literature from the period 1800-1922 (Underwoodet al., 2015); (ii) abstracts from the High Energy Physics arXiv repository (Clementet al., 2019). We obtain some historically well-known changepoints and discover some new ones.

Independent Component Analysis (ICA) is intended to recover the mutually independent sources from their linear mixtures, and F astICA is one of the most successful ICA algorithms. Although it seems reasonable to improve the performance of F astICA by introducing more nonlinear functions to the negentropy estimation, the original fixed-point method (approximate Newton method) in F astICA degenerates under this circumstance. To alleviate this problem, we propose a novel method based on the second-order approximation of minimum discrimination information (MDI). The joint maximization in our method is consisted of minimizing single weighted least squares and seeking unmixing matrix by the fixed-point method. Experimental results validate its efficiency compared with other popular ICA algorithms.

The Bayesian brain hypothesis postulates that the brain accurately operates on statistical distributions according to Bayes' theorem. The random failure of presynaptic vesicles to release neurotransmitters may allow the brain to sample from posterior distributions of network parameters, interpreted as epistemic uncertainty. It has not been shown previously how random failures might allow networks to sample from observed distributions, also known as aleatoric or residual uncertainty. Sampling from both distributions enables probabilistic inference, efficient search, and creative or generative problem solving. We demonstrate that under a population-code based interpretation of neural activity, both types of distribution can be represented and sampled with synaptic failure alone. We first define a biologically constrained neural network and sampling scheme based on synaptic failure and lateral inhibition. Within this framework, we derive dropout based epistemic uncertainty, then prove an analytic mapping from synaptic efficacy to release probability that allows networks to sample from arbitrary, learned distributions represented by a receiving layer. Second, our result leads to a local learning rule by which synapses adapt their release probabilities. Our result demonstrates complete Bayesian inference, related to the variational learning method of dropout, in a biologically constrained network using only locally-learned synaptic failure rates. Introduction The Bayesian Brain hypothesis has led to a number of important insights about neural coding in the brain (Knill and Pouget, 2004; Friston, 2010, 2012; Pouget et al., 2013; Lee and Mumford, 2003) by characterizing neural representation and processing in terms of formal probabilistic inference and sampling. Furthermore, the introduction of related probabilistic representations and sampling processes in modern deep learning variational models has led to improved performance on a range of different tasks (Zhang et al., 2019; Blei et al., 2017; Kingma and Welling, 2014; Detorakis et al., 2019). The widely-used dropout technique in deep learning can be seen as a form of variational inference and sampling (Srivastava et al., 2014; Gal and Ghahramani, 2016) with direct analogy to the random failure of synapses in the brain. This link has led to biologically-motivated models of variational deep learning that use network weight dropout to simulate synaptic failure (Mostafa and Cauwenberghs, 2018; Wan et al., 2013; Neftci et al., 2016). In this paper, we build on these and other recent findings in machine learning and neurobiology to show how the brain can accurately represent the two primary components of probabilistic inference, distributions of observed data and distributions of unobserved values (such as model parameters), with the single, biologically established mechanism of synaptic failure.